Refining the ambiguity domain characteristics of non-stationary signals for improved time–frequency analysis: Test case of multidirectional and multicomponent piecewise LFM and HFM signals

Abstract

This paper aims at providing a more accurate description of the ambiguity domain characteristics of a piecewise multicomponent non-stationary signals with focus on piece-wise linear frequency modulated (LFM) (PW-LFM) signal and a mixed LFM and hyperbolic FM (HFM). The main motivation comes from the observed PW-LFM nature of several real life signals. It is essential that the characteristics of these types of signals be taken into account for the design of high resolution Time–Frequency Distributions (TFDs) and therefore to improve the application and interpretation of time–frequency signal analysis and processing. In this paper the ambiguity function (AF) of a general PW-LFM signal is derived exactly and then analyzed to deduce important properties. The precise location and behavior of both auto-terms and cross-terms of a general piecewise LFM signal can be deduced from its AF. Numerical simulations using different types of test signals confirm the analytical derivations. An extension of the PW-LFM test signal is also presented by using HFM signals. For such signals, the exact analytical expression of auto-terms is given as well as the expression of cross-terms between HFM and LFM. The results obtained can be used in future studies to design more advanced quadratic time–frequency distributions (QTFDs) that exhibit improved properties in terms of resolution and accuracy.